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Annulus Area (Ring)

Also known as area of an annulus · area between two circles · pipe wall area · donut area

A=π(R2−r2)A = \pi (R^2 - r^2)

Worked example: R = 5 m, r = 3 m → 16 pi m^2 — press Try an example to run it live, then adjust anything.

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Constant used — built into this formula, no need to enter
π=3.141592653589793\pi = 3.141592653589793Pi · exact
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Annulus Area (Ring) explained

RrA

An annulus is the washer shape between two concentric circles, and its area is simply the big disc minus the small one: A=π(R2−r2)A = \pi(R^2 - r^2). This is the cross-section of every pipe wall, every tube, every ring gasket. A pipe with a 100 mm outer radius and 94 mm inner radius has a wall cross-section of π(0.01−0.008836)≈0.00366\pi(0.01 - 0.008836) \approx 0.00366 m², which is the number that sets its strength and its weight per metre.

Note the difference between this and the flow area: water travels through πr2\pi r^2, the inner circle, while the steel occupies the annulus around it. Confusing the two is a classic sizing error.

Annulus Area (Ring) formula

A=π(R2−r2)A = \pi (R^2 - r^2)
Where
  • AA= Area (m²)
  • RR= Outer radius (m)
  • rr= Inner radius (m)

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